Question

1. solve for the x-values of the x-intercepts of the parabola whose equation is $y = x^2 - x - 6$. write all solutions on the same line, separated by commas. enter your next step here

Explanation:

Step1: Find x-intercepts (set y=0)

To find the x - intercepts of the parabola given by the equation \(y = x^{2}-x - 6\), we set \(y = 0\). So we have the quadratic equation:
\(x^{2}-x - 6=0\)

Step2: Factor the quadratic equation

We factor the quadratic expression \(x^{2}-x - 6\). We need two numbers that multiply to \(- 6\) and add up to \(-1\). The numbers are \(-3\) and \(2\) since \((-3)\times2=-6\) and \(-3 + 2=-1\). So we can factor the quadratic as:
\((x - 3)(x+2)=0\)

Step3: Solve for x using zero - product property

The zero - product property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\). So, for \((x - 3)(x + 2)=0\), we set each factor equal to zero:

• If \(x-3=0\), then \(x = 3\).
• If \(x + 2=0\), then \(x=-2\).

Answer:

-2, 3